As for glue. I would also recommend super glue for emerald to emerald. Just make sure they are super clean and dry.
Super glue is amazing. I once had a button on a knitted wool coat break in half. I glued it back together with a wool fiber in between and it never broke again although it was washed and worn for at least two more winters. You had to look very closely to see that anything was amiss.
The hypo cement is great for finishing off knots and anything where you need a slight amount of give after the glue is dry. It's made for gluing crystals to the face of a watch so they can be removed later, so it isn't a good choice for a permanent bond on two hard surfaces. It worked great on gluing tiny pearls into my octopus earrings, but I would never use it on a ring.
The E6000 is interesting stuff. It really sticks disparate things together well and is stretchy. You have to yank hard to get things apart. I know this because I didn't trust how well it would hold so I tested it after it was dry.
Bob's head was glued with E6000...
